Abstract Despite attempts at reconciliation, the role of omnivory in food web stability remains unclear. Here we develop a novel community matrix approach that is analogous to the bifurcation method of modular food web theory to show that the stability of omnivorous food chains depends critically on interaction strength. We find that there are only six possible ways that omnivorous interaction strengths can influence the stability of linear food chains. The results from these six cases suggest that: (1) strong omnivory is always destabilizing, (2) stabilization by weak to intermediate omnivorous interaction strengths dominates the set of possible stability responses, and, (3) omnivory can be occasionally strictly destabilizing or intermittently destabilizing. We then revisit the classical results of Pimm and Lawton to show that although their parameterization tends to produce a low percentage of stable omnivorous webs, the same parameterization shows strong theoretical support for the weak interaction effect. Finally, we end by arguing that our current empirical knowledge of omnivory resonates with this general theory.